On the uniform distribution modulo one of subsequences of polynomial sequences II
β Scribed by Jean Coquet
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 246 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
A famous inequality of ErdΓΆs and TurΓ‘n estimates the discrepancy \(\Delta\) of a finite sequence of real numbers by the quantity \(B=\min _{K} K^{-1}+\sum_{k=1}^{K-1}\left|\alpha_{k}\right| / k\), where the \(\alpha_{k}\) are the Fourier coefficients. We investigate how bad this estimate can be. We
In this paper, we prove: "Suppose \(\alpha\) is an irrational number and let \(\|y\|\) denote the smallest distance of \(y\) from an integer. Then, for any real number \(\beta\), there are infinitely many primes \(p\) such that \(\|\alpha p-\beta\|<p^{-4 / 13}\)." 1993 Academic Press, Inc.